{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figures and Tables for Welfare Analysis\n",
    "\n",
    "This notebook reproduces Table 10 and 11 of the Paper, the welfare effects of a price difference, as well as Figures found in Appendix F (F.1). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np \n",
    "from importlib import reload\n",
    "import pandas as pd\n",
    "import pickle\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.optimize import bisect\n",
    "from functools import partial\n",
    "from itertools import product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "module_path = os.path.abspath(os.path.join('..'))\n",
    "if module_path not in sys.path:\n",
    "    sys.path.append(module_path)\n",
    "    \n",
    "from model import micro, macro, params \n",
    "from model import distributions as dist\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pus_ge</th>\n",
       "      <th>peu_ge</th>\n",
       "      <th>peu_pe</th>\n",
       "      <th>aeu_ge</th>\n",
       "      <th>aeu_pe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>m</th>\n",
       "      <td>0.557813</td>\n",
       "      <td>0.594078</td>\n",
       "      <td>0.580346</td>\n",
       "      <td>0.538612</td>\n",
       "      <td>0.539985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>4.229094</td>\n",
       "      <td>4.270291</td>\n",
       "      <td>4.270291</td>\n",
       "      <td>3.687379</td>\n",
       "      <td>4.270291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>2.297478</td>\n",
       "      <td>2.458274</td>\n",
       "      <td>2.317035</td>\n",
       "      <td>1.988302</td>\n",
       "      <td>2.003603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k</th>\n",
       "      <td>27.199406</td>\n",
       "      <td>27.895348</td>\n",
       "      <td>27.221799</td>\n",
       "      <td>23.68989</td>\n",
       "      <td>23.902514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n</th>\n",
       "      <td>1.327392</td>\n",
       "      <td>1.327392</td>\n",
       "      <td>1.327392</td>\n",
       "      <td>1.327392</td>\n",
       "      <td>1.327392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s</th>\n",
       "      <td>0.131899</td>\n",
       "      <td>0.104429</td>\n",
       "      <td>0.102976</td>\n",
       "      <td>0.146069</td>\n",
       "      <td>0.109549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>csy</th>\n",
       "      <td>0.675154</td>\n",
       "      <td>0.680098</td>\n",
       "      <td>0.650683</td>\n",
       "      <td>0.685288</td>\n",
       "      <td>0.651058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ksy</th>\n",
       "      <td>6.431497</td>\n",
       "      <td>6.532423</td>\n",
       "      <td>6.374694</td>\n",
       "      <td>6.424588</td>\n",
       "      <td>5.597397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h</th>\n",
       "      <td>0.899511</td>\n",
       "      <td>0.92392</td>\n",
       "      <td>0.920364</td>\n",
       "      <td>0.875535</td>\n",
       "      <td>0.877631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>g2</th>\n",
       "      <td>1.147230</td>\n",
       "      <td>1.120584</td>\n",
       "      <td>1.123534</td>\n",
       "      <td>1.171403</td>\n",
       "      <td>1.168196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>g3</th>\n",
       "      <td>1.236394</td>\n",
       "      <td>1.174843</td>\n",
       "      <td>1.182866</td>\n",
       "      <td>1.296893</td>\n",
       "      <td>1.291185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>g4</th>\n",
       "      <td>1.273114</td>\n",
       "      <td>1.189868</td>\n",
       "      <td>1.200539</td>\n",
       "      <td>1.359954</td>\n",
       "      <td>1.351465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tgood</th>\n",
       "      <td>0.969140</td>\n",
       "      <td>0.969157</td>\n",
       "      <td>0.969146</td>\n",
       "      <td>0.969139</td>\n",
       "      <td>0.969139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tbad</th>\n",
       "      <td>0.276073</td>\n",
       "      <td>0.374573</td>\n",
       "      <td>0.356467</td>\n",
       "      <td>0.217226</td>\n",
       "      <td>0.221194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r</th>\n",
       "      <td>0.010871</td>\n",
       "      <td>0.010114</td>\n",
       "      <td>0.010871</td>\n",
       "      <td>0.011108</td>\n",
       "      <td>0.010871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>w</th>\n",
       "      <td>1.964627</td>\n",
       "      <td>1.979274</td>\n",
       "      <td>1.964627</td>\n",
       "      <td>1.709903</td>\n",
       "      <td>1.806222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tax</th>\n",
       "      <td>0.202095</td>\n",
       "      <td>0.146553113750822</td>\n",
       "      <td>0.202095</td>\n",
       "      <td>0.20534695392508662</td>\n",
       "      <td>0.202095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>oop</th>\n",
       "      <td>0.076092</td>\n",
       "      <td>0.060832</td>\n",
       "      <td>0.059426</td>\n",
       "      <td>0.073473</td>\n",
       "      <td>0.055293</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          pus_ge             peu_ge     peu_pe               aeu_ge     aeu_pe\n",
       "m       0.557813           0.594078   0.580346             0.538612   0.539985\n",
       "y       4.229094           4.270291   4.270291             3.687379   4.270291\n",
       "c       2.297478           2.458274   2.317035             1.988302   2.003603\n",
       "k      27.199406          27.895348  27.221799             23.68989  23.902514\n",
       "n       1.327392           1.327392   1.327392             1.327392   1.327392\n",
       "s       0.131899           0.104429   0.102976             0.146069   0.109549\n",
       "csy     0.675154           0.680098   0.650683             0.685288   0.651058\n",
       "ksy     6.431497           6.532423   6.374694             6.424588   5.597397\n",
       "h       0.899511            0.92392   0.920364             0.875535   0.877631\n",
       "g2      1.147230           1.120584   1.123534             1.171403   1.168196\n",
       "g3      1.236394           1.174843   1.182866             1.296893   1.291185\n",
       "g4      1.273114           1.189868   1.200539             1.359954   1.351465\n",
       "tgood   0.969140           0.969157   0.969146             0.969139   0.969139\n",
       "tbad    0.276073           0.374573   0.356467             0.217226   0.221194\n",
       "r       0.010871           0.010114   0.010871             0.011108   0.010871\n",
       "w       1.964627           1.979274   1.964627             1.709903   1.806222\n",
       "tax     0.202095  0.146553113750822   0.202095  0.20534695392508662   0.202095\n",
       "oop     0.076092           0.060832   0.059426             0.073473   0.055293"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aggs = pd.read_pickle('output/table_10-11_aggregates.pkl')\n",
    "scenarios = aggs.columns\n",
    "aggs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "eqs_temp = []\n",
    "opt_temp = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "scenarios = ['pus_ge','peu_ge','peu_pe','aeu_ge','aeu_pe']\n",
    "\n",
    "for scn in scenarios:\n",
    "    file = open('output/eq_'+scn+'3.pkl','rb')\n",
    "    eq = pickle.load(file)\n",
    "    file.close()\n",
    "    eqs_temp.append(eq)\n",
    "    opt = pd.read_pickle('output/opt_'+scn+'3.pkl')\n",
    "    opt_temp.append(opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "eqs  = dict(zip(scenarios,eqs_temp))\n",
    "opts = dict(zip(scenarios,opt_temp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing WTP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "gridk = eqs['pus_ge'].stats.gridk\n",
    "ne, nk, nh = eqs['pus_ge'].stats.ne, eqs['pus_ge'].stats.nk, eqs['pus_ge'].stats.nh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dif(k,fb,fj):\n",
    "    return fj(k) - fb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "for scn in scenarios[1:]:\n",
    "    opts[scn]['wtp'] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "for e in range(ne):\n",
    "    for h in range(nh):\n",
    "        cond = (opts['pus_ge'].e == e) & (opts['pus_ge'].h == h)\n",
    "        vb = opts['pus_ge'].loc[cond,'v'] #peu_ge\n",
    "        fb = interp1d(gridk,vb,kind='cubic')\n",
    "        for scn in scenarios[1:]:\n",
    "            vj = opts[scn].loc[cond,'v'] #pus_ge\n",
    "            fj = interp1d(gridk,vj,kind='cubic')\n",
    "            for i,k in enumerate(gridk):\n",
    "                if scn=='aeu_ge' or scn=='aeu_pe':\n",
    "                    lim = [k,gridk[-1]]\n",
    "                else :\n",
    "                    lim = [0,k]\n",
    "                d = partial(dif,fb=fb(k),fj=fj)\n",
    "                try:\n",
    "                    kp = bisect(d,lim[0],lim[1],disp=False)\n",
    "                except (RuntimeError, TypeError, NameError,ValueError):\n",
    "                    kp = np.nan\n",
    "                    pass\n",
    "                wtp = k - kp # kp - k\n",
    "                opts[scn].loc[cond & (opts[scn].k == i),'wtp'] = wtp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "for scn in scenarios[1:]:\n",
    "    opts[scn]['wtpfl'] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The fixed value is the one of US with peu price <=> the higher utility\n",
    "# => how much I must give to the losers (those in the benchmark) to compensate their lower utility \n",
    "\n",
    "for e in range(ne):\n",
    "    for h in range(nh):\n",
    "        cond = (opts['pus_ge'].e == e) & (opts['pus_ge'].h == h)\n",
    "        vb = opts['peu_ge'].loc[cond,'v'] #peu_ge\n",
    "        fb = interp1d(gridk,vb,kind='cubic')\n",
    "        vj = opts['pus_ge'].loc[cond,'v'] #pus_ge\n",
    "        fj = interp1d(gridk,vj,kind='cubic')\n",
    "        for i,k in enumerate(gridk):\n",
    "            lim = [k,gridk[-1]]\n",
    "            d = partial(dif,fb=fb(k),fj=fj)\n",
    "            try:\n",
    "                kp = bisect(d,lim[0],lim[1],disp=False)\n",
    "            except (RuntimeError, TypeError, NameError,ValueError):\n",
    "                kp = np.nan\n",
    "                pass\n",
    "            wtpfl = kp - k \n",
    "            opts['peu_ge'].loc[cond & (opts['peu_ge'].k == i),'wtpfl'] = wtpfl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The fixed value is the one of US with peu price <=> the higher utility\n",
    "# => how much I must give to the losers (those in the benchmark) to compensate their lower utility \n",
    "\n",
    "for e in range(ne):\n",
    "    for h in range(nh):\n",
    "        cond = (opts['pus_ge'].e == e) & (opts['pus_ge'].h == h)\n",
    "        vb = opts['peu_pe'].loc[cond,'v'] #peu_ge\n",
    "        fb = interp1d(gridk,vb,kind='cubic')\n",
    "        vj = opts['pus_ge'].loc[cond,'v'] #pus_ge\n",
    "        fj = interp1d(gridk,vj,kind='cubic')\n",
    "        for i,k in enumerate(gridk):\n",
    "            lim = [k,gridk[-1]]\n",
    "            d = partial(dif,fb=fb(k),fj=fj)\n",
    "            try:\n",
    "                kp = bisect(d,lim[0],lim[1],disp=False)\n",
    "            except (RuntimeError, TypeError, NameError,ValueError):\n",
    "                kp = np.nan\n",
    "                pass\n",
    "            wtpfl = kp - k \n",
    "            opts['peu_pe'].loc[cond & (opts['peu_pe'].k == i),'wtpfl'] = wtpfl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The fixed value is the one of US with aus TFP <=> the higher utility \n",
    "# => how much I must take to the winners to overcompensate their higher utility \n",
    "\n",
    "for e in range(ne):\n",
    "    for h in range(nh):\n",
    "        cond = (opts['pus_ge'].e == e) & (opts['pus_ge'].h == h)\n",
    "        vb = opts['pus_ge'].loc[cond,'v'] #peu_ge\n",
    "        fb = interp1d(gridk,vb,kind='cubic')\n",
    "        vj = opts['aeu_ge'].loc[cond,'v'] #pus_ge\n",
    "        fj = interp1d(gridk,vj,kind='cubic')\n",
    "        for i,k in enumerate(gridk):\n",
    "            lim = [k,gridk[-1]]#lim = [0,k]\n",
    "            d = partial(dif,fb=fb(k),fj=fj)\n",
    "            try:\n",
    "                kp = bisect(d,lim[0],lim[1],disp=False)\n",
    "            except (RuntimeError, TypeError, NameError,ValueError):\n",
    "                kp = np.nan\n",
    "                pass\n",
    "            wtpfl = k - kp \n",
    "            opts['aeu_ge'].loc[cond & (opts['aeu_ge'].k == i),'wtpfl'] = wtpfl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The fixed value is the one of US with aus TFP <=> the higher utility \n",
    "# => how much I must take to the winners to overcompensate their higher utility \n",
    "\n",
    "for e in range(ne):\n",
    "    for h in range(nh):\n",
    "        cond = (opts['pus_ge'].e == e) & (opts['pus_ge'].h == h)\n",
    "        vb = opts['pus_ge'].loc[cond,'v'] #peu_ge\n",
    "        fb = interp1d(gridk,vb,kind='cubic')\n",
    "        vj = opts['aeu_pe'].loc[cond,'v'] #pus_ge\n",
    "        fj = interp1d(gridk,vj,kind='cubic')\n",
    "        for i,k in enumerate(gridk):\n",
    "            lim = [k,gridk[-1]]#lim = [0,k]\n",
    "            d = partial(dif,fb=fb(k),fj=fj)\n",
    "            try:\n",
    "                kp = bisect(d,lim[0],lim[1],disp=False)\n",
    "            except (RuntimeError, TypeError, NameError,ValueError):\n",
    "                kp = np.nan\n",
    "                pass\n",
    "            wtpfl = k - kp \n",
    "            opts['aeu_pe'].loc[cond & (opts['aeu_pe'].k == i),'wtpfl'] = wtpfl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "degpol = 8\n",
    "hs = [0,1]\n",
    "es = [0,4,9]\n",
    "elabels = ['low','middle','high']\n",
    "hlabels = ['bad health','good health']\n",
    "hcolors = ['darkgray','black']\n",
    "for i,e in enumerate(es):\n",
    "    plt.figure()\n",
    "    for h in hs:\n",
    "        cond = (opts['pus_ge'].e == e) & (opts['pus_ge'].h == h)\n",
    "        wtps = opts['peu_ge'].loc[cond,'wtpfl']\n",
    "        wtps.index = np.arange(len(wtps))\n",
    "        ws = wtps.loc[wtps.isna()==False]\n",
    "\n",
    "        ks = gridk[ws.index.values]\n",
    "        p = np.polyfit(ks, ws, deg=degpol)#4)\n",
    "        w = np.poly1d(p)\n",
    "        plt.plot(ks,[w(k) for k in ks],color=hcolors[h],label=hlabels[h]+' (ge)')\n",
    "        \n",
    "        wtps = opts['peu_pe'].loc[cond,'wtpfl']\n",
    "        wtps.index = np.arange(len(wtps))\n",
    "        ws = wtps.loc[wtps.isna()==False]\n",
    "        ks = gridk[ws.index.values]\n",
    "        p = np.polyfit(ks, ws, deg=degpol)#4)\n",
    "        w = np.poly1d(p)\n",
    "        plt.plot(ks,[w(k) for k in ks],'--',color=hcolors[h],label=hlabels[h]+' (pe)')\n",
    "    plt.xlabel('asset (a)')\n",
    "    plt.ylabel('willingness to pay')\n",
    "    plt.legend() \n",
    "    plt.savefig('../figures/fig_f1_wtp_price_'+elabels[i]+'.eps')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cost-of-Living Index\n",
    "\n",
    "The price index is based on the follownig formula\n",
    "$$\n",
    "I_{LC}(a,h,e) = \\frac{{\\cal \\hat{E}}_{US}}{{\\cal E}_{EU}} = \\frac{a + {\\cal P} + G_{p=p_{EU}}}{a + G_{p=p_{EU}}} \n",
    "~~\\Rightarrow~~ \n",
    "I_{LC}(h,e) = \\sum_a \\frac{a + {\\cal P} + G_{p=p_{EU}}}{a + G_{p=p_{EU}}} \\lambda(a)\n",
    "$$\n",
    "because the costs of living are \n",
    "$$\n",
    "{\\cal E}_{EU} = a + G_{p=p_{EU}}\n",
    "$$\n",
    "for an individual living in a economy where $p=p_{EU}$ and with the endovment $a + G_{p=p_{EU}}$ and \n",
    "$$\n",
    "{\\cal \\hat{E}}_{US} = a + {\\cal P} + G_{p=p_{EU}}\n",
    "$$\n",
    "for an individual living in a economy where $p=p_{US}$ and with the same endovment $a + G_{p=p_{EU}}$\n",
    "\n",
    "Remark: it is necessary to control for the changes in $G$ in order to have two individuals with the same endovments. This leads to define ${\\cal \\hat{E}}_{US}$ which is different from the standard expenditure function\n",
    "$$\n",
    "{\\cal \\hat{E}}_{US} \\neq {\\cal E}_{US} = a + {\\cal P} + G_{p=p_{US}}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Human Wealth Calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "ge = np.zeros((ne,len(scenarios)))\n",
    "for i,scn in enumerate(scenarios):\n",
    "    pi = eqs[scn].inc.tprob\n",
    "    ri = 1/(1+aggs.loc['r',scn])\n",
    "    res   = np.eye(ne) - ri*pi\n",
    "    ires   = np.linalg.inv(res)\n",
    "    ge[:,i] = (1-aggs.loc['tax',scn])*aggs.loc['w',scn]*(ires@np.exp(eqs[scn].inc.pte))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cost of Living Calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "for scn in scenarios[1:]:\n",
    "    opts[scn]['ilt'] = 0.0\n",
    "    opts[scn]['ge']  = 0.0\n",
    "\n",
    "for i in opts['pus_ge'].index:   \n",
    "    for j,scn in enumerate(scenarios[1:]):\n",
    "        col_ref = gridk[opts['pus_ge'].loc[i,'k']] + opts[scn].loc[i,'wtpfl'] + ge[opts[scn].loc[i,'e'],1+j]\n",
    "        col     = gridk[opts[scn].loc[i,'k']] + ge[opts[scn].loc[i,'e'],1+j]\n",
    "        cc_ref  = gridk[opts['pus_ge'].loc[i,'k']] + opts[scn].loc[i,'wtpfl']\n",
    "        cc      = gridk[opts['pus_ge'].loc[i,'k']]\n",
    "        opts[scn].loc[i,'ge']      = ge[opts['pus_ge'].loc[i,'e'],0]/ge[opts[scn].loc[i,'e'],1+j]\n",
    "        opts[scn].loc[i,'col']     = col\n",
    "        opts[scn].loc[i,'col_ref'] = col_ref        \n",
    "        opts[scn].loc[i,'ilt']     = (col_ref/col)*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "es = [0,4,9]\n",
    "columns = ['0','4','9','Total']\n",
    "hs = [0,1]\n",
    "equ = ['ge','pe']\n",
    "ll = [equ,hs]\n",
    "rows = list(product(*ll))\n",
    "index = pd.MultiIndex.from_tuples(rows, names=['equilibrium','health'])\n",
    "table_p = pd.DataFrame(index=index,columns=columns)\n",
    "for q in equ:\n",
    "    for j,e in enumerate(es):\n",
    "        for h in hs:\n",
    "            cond = (opts['peu_'+q].e == e) & (opts['peu_'+q].h == h)\n",
    "            sel  = opts['peu_'+q].loc[cond,['ps','ilt']]\n",
    "            sel  = sel.loc[sel['ilt'].isna()!=True,:]\n",
    "            sel['ps'] = sel['ps']/sel['ps'].sum()\n",
    "            sel['p']  = sel['ps']*sel['ilt']\n",
    "            table_p.loc[(q,h),columns[j]] = sel['p'].sum()\n",
    "    sel = opts['peu_'+q].loc[:,['ps','ilt']]\n",
    "    sel = sel.loc[sel['ilt'].isna()!=True,:]\n",
    "    sel['ps'] = sel['ps']/sel['ps'].sum()\n",
    "    sel['p'] = sel['ps']*sel['ilt']\n",
    "    table_p.loc[(q,0),columns[-1]] = sel['p'].sum()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>4</th>\n",
       "      <th>9</th>\n",
       "      <th>Total</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>equilibrium</th>\n",
       "      <th>health</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">ge</th>\n",
       "      <th>0</th>\n",
       "      <td>100.479095</td>\n",
       "      <td>101.975579</td>\n",
       "      <td>103.53165</td>\n",
       "      <td>102.234567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100.999855</td>\n",
       "      <td>102.117013</td>\n",
       "      <td>103.31336</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">pe</th>\n",
       "      <th>0</th>\n",
       "      <td>100.075325</td>\n",
       "      <td>100.632447</td>\n",
       "      <td>101.240347</td>\n",
       "      <td>100.577746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100.236982</td>\n",
       "      <td>100.521883</td>\n",
       "      <td>101.032383</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             0           4           9       Total\n",
       "equilibrium health                                                \n",
       "ge          0       100.479095  101.975579   103.53165  102.234567\n",
       "            1       100.999855  102.117013   103.31336         NaN\n",
       "pe          0       100.075325  100.632447  101.240347  100.577746\n",
       "            1       100.236982  100.521883  101.032383         NaN"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Table 11. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "table_p.round(3).to_latex('../tables/table_11_col_index.tex')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Willingness to Pay for a Price Change\n",
    "\n",
    "Compiling the table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "es = [0,4,9]\n",
    "columns = ['0','4','9','Total']\n",
    "hs = [0,1]\n",
    "equ = ['ge','pe']\n",
    "ll = [equ,hs]\n",
    "rows = list(product(*ll))\n",
    "index = pd.MultiIndex.from_tuples(rows, names=['equilibrium','health'])\n",
    "table_w = pd.DataFrame(index=index,columns=columns)\n",
    "for q in equ:\n",
    "    for j,e in enumerate(es):\n",
    "        for h in hs:\n",
    "            cond = (opts['peu_'+q].e == e) & (opts['peu_'+q].h == h)\n",
    "            sel  = opts['peu_'+q].loc[cond,['ps','wtpfl','c']]\n",
    "            sel  = sel.loc[sel['wtpfl'].isna()!=True,:]\n",
    "            sel['ps'] = sel['ps']/sel['ps'].sum()\n",
    "            sel['Awtpfl']  = (sel['ps']*sel['wtpfl']).sum()\n",
    "            sel['wtpc']    = ((sel['ps']*sel['wtpfl']).sum())/((sel['ps']*opts['pus_ge'].loc[cond,'c']).sum())\n",
    "            table_w.loc[(q,h),columns[j]] = sel['wtpc'].loc[sel['wtpc'].index[0]]\n",
    "    sel = opts['peu_'+q].loc[:,['ps','wtpfl','c']]\n",
    "    sel = sel.loc[sel['wtpfl'].isna()!=True,:]\n",
    "    sel['ps'] = sel['ps']/sel['ps'].sum()\n",
    "    sel['Awtpfl']  = (sel['ps']*sel['wtpfl']).sum()\n",
    "    sel['wtpc']    = ((sel['ps']*sel['wtpfl']).sum())/((sel['ps']*opts['pus_ge'].loc[:,'c']).sum())\n",
    "    table_w.loc[(q,0),columns[-1]] = sel['wtpc'].loc[sel['wtpc'].index[0]]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>4</th>\n",
       "      <th>9</th>\n",
       "      <th>Total</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>equilibrium</th>\n",
       "      <th>health</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">ge</th>\n",
       "      <th>0</th>\n",
       "      <td>2.242532</td>\n",
       "      <td>3.120702</td>\n",
       "      <td>2.545802</td>\n",
       "      <td>2.542036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.168093</td>\n",
       "      <td>2.601782</td>\n",
       "      <td>2.347443</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">pe</th>\n",
       "      <th>0</th>\n",
       "      <td>0.311334</td>\n",
       "      <td>0.896056</td>\n",
       "      <td>0.824207</td>\n",
       "      <td>0.60348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.451886</td>\n",
       "      <td>0.576324</td>\n",
       "      <td>0.677176</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           0         4         9     Total\n",
       "equilibrium health                                        \n",
       "ge          0       2.242532  3.120702  2.545802  2.542036\n",
       "            1       2.168093  2.601782  2.347443       NaN\n",
       "pe          0       0.311334  0.896056  0.824207   0.60348\n",
       "            1       0.451886  0.576324  0.677176       NaN"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Table 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "table_w.round(3).to_latex('../tables/table_10_wtp.tex')"
   ]
  }
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